So first off, the image you provided is Bas Relief, or Low Relief, not high. High looks more like standalone statues, except attached to the surface.
As for the question itself, that depends on the medium, tools, complexity of design, and your skill as a maker. Having done inlay, engraving, and bas relief, in wood, stone, and metal, here’s my experience:
in general, I’ve found relief to be more time consuming than engraving, as there’s just more detail and more material to remove. If you take that to mean “more difficult” then there’s your answer, but ymmv.
Between media, generally the harder the material, the longer it takes, but the more forgiving it is of minor mistakes. Hit a piece of white oak at the wrong angle, you get a bad looking mark. Hit a piece of softwood wrong, the whole thing splits.
Rock I’m less versed in, but same rules tend to apply. Choose your piece carefully, don’t fight the grain, work with it, make the design compliment it.
In metal, engraving is substantially easier, as you can acid etch or use electrolysis. Relief will need power tools or a set of scribes, chisels, hammers, and assorted shaping hand tools (look up hobo nickels to get an idea of the process).
For any medium, a small rotary tool has a lot of power and can remove material quickly, but can slip and scar the workpiece. I tend to rough out designs with the dremel then refine with chisels and files to reach the final look.
For all media, remember: This is a subtractive art. Once material is removed, it ain’t coming back (unless you weld more metal on, but that’s not always viable). Be careful and considerate of the process, but also remember the Japanese philosophy of Wabi Sabi, or acceptance of imperfection. You are making something by hand, and hands are imperfect machines. Even a master craftsman cannot escape this. You want perfect, just order one from a factory.